---

Compressor power requirement

Follow us on Twitter 
Question, remark ? Contact us at contact@myengineeringtools.com

---

Section summary
1. Formula to calculate the compressor power required
2. Usual values for calculation
3. Example of calculation
4. Compressor power free Excel calculation tool

---

1. Formula : compressor power calculation

1.1 Simplified formula

For 1 compressor stage of a perfect gas, the isentropic compression is the following :

P_is = 2.31*(k/(k-1))*(T_dis-T_suct)/M*Q_m

Equation 1 : simplified compression power calculation formula

A compression is said isentropic when it is carried out by an ideal compressor, without friction, without internal leakage and while being perfectly insulated. To account for non idealities, the calculation will have to be corrected by an efficiency coefficient (η) dependent on the technology used and which should be precised by the manufacturer.

With :

P_is=Power (kW)
T_suct=Temperature inlet compressor (K)
T_discharge=Temperature outlet compressor (K)
M=Molar weight of gas (g/mol)
Q_m=Compressor throughput (t/h)
k=Gas isentropic coefficient

>>> To know more about this formula please follow this link <<<

One will note that a key unknown in the equation above is the discharge temperature. The discharge temperature T_discharge can be determined thanks to an abacus or by calculation, for an isentropic compression, please have a look to this page.

1.2 General formula with gas compressibility factor

The following formula can be used for high compression ratio and high temperature ratios that prevent to assume the gas is perfect and its compressibility factor is ~1 :

P_is = (k*Z*R*T₁)/(k-1)*[(P₂/P₁)^(k-1)/k-1]*Q_m

With : P_is=Power (kW)
Z = gas compressibility factor (can be defined on an Amagat diagram by calculating the reduced pressure and reduced temperature of the gas)
P₁ = Pressure inlet compressor (kPa)
P₂ = Pressure outlet compressor (kPa)
Q_m=Compressor throughput (kg/s)
k=Gas isentropic coefficient
R = [8314/molecular weight (J/(kg.K))]/1000 = 8.314 / molecular weight

>>> To know more about this formula please follow this link <<<

The power calculated must also be corrected by an efficiency coefficient given by the manufacturer of the compressor considered.

Also about compressor calculations on MyEngineeringTools.com Compressor Power formula explained ! Reciprocating compressor capacity Temperature rise in a compressor Polytropic compression Compressors head and flow coefficients, compression ratio

2. Usual values for calculations

• For air k=1.4
• Reciprocating compressor high compression rate η=0.75
• Reciprocating compressor low compression rate η=0.75
• Rotary compressors η=0.7

Centrifugal compressors : η is calculated from the polytropic efficiency given by the manufacturer. A chart is then used to calculate the polytropic coefficient of the gas, then the discharge temperature calculated and then the actual power needed thanks to the formula 1 above.

For references of industrial compressors and discussions with experts, the reader can refer to the following company (no link with MyEngineeringTools.com) :

www.continental-industrie.com

3. Example of calculation of the compression power

A compressor has to deliver 2000 Nm3/h of air at 6 bar g, from air at atmospheric pressure and 20°c. The efficiency of the compressor is known and is 0.72.

Step 1 : calculate the mass flow rate

The compressor is to deliver 2000 Nm3/h of air. Normal conditions are here defined as 101325 Pa and 0°c [1], at this pressure gas ideality is mostly verified thus the specific gravity is PM/RT/1000 = 1.294 kg/m3. This gives a mass flowrate of 2000*1.294 = 2587 kg/h.

STEP 2 : calculate the discharge temperature

The discharge temperature for an isentropic compression can be calculated with :

In this case T_discharge = (20+273.15)*((101325+6*100000)/101325)^((1.4-1)/1.4) = 509.5 K

Which gives 509.5 - 273.15 = 236.4c

STEP 3 : calculate the isentropic power requirement

Use the formula given above : P_is = 2.31*1.4/(1.4-1)*(236.4-20)/29*2587 / 1000 = 156 kW

STEP 4 : calculate the actual power requirement

The efficiency of the compressor must be taken into consideration and is equal to 0.72 which gives a required power of 156/0.72 = 216.8 kW.

4. Free Excel calculation tool : Compressor calculator

You can access a free compressor calculator Excel to make the compressor power calculation explained above : Compressor Power Calculator (click here)

Warning : this calculator is provided to illustrate the concepts mentionned in this webpage, it is not intended for detail design. It is not a commercial product, no guarantee is given on the results. Please consult a reputable designer for all detail design you may need.

---

Source

[1] https://en.wikipedia.org/wiki/Standard_cubic_feet_per_minute

[Perry] Perry's Chemical Engineer's Handbook, Section 10 Transport and storage of fluids, page 10-45, McGraw-Hill, 2008